This invention relates to a method for determining the road handling of a tyre of a wheel for a vehicle.
At the present time, to determine the road handling performance of a tyre, the manufacturers of pneumatic tyres are obliged to produce numerous physical prototypes in order to experimentally evaluate the effects of the various design parameters on the drift behaviour of the tyre, under steady state and transient state conditions. The experimental tests are conducted according to iterative procedures, that are largely empirical and based on experience and are also extremely demanding in terms of time and cost.
Furthermore, automobile manufacturing companies are insisting more and more frequently that the makers of pneumatic tyres come up with tyres with extremely precise technical characteristics as early as the initial stages of vehicle study and dynamic behaviour forecasting.
In such a position, the tyre manufacturers are finding it very difficult to respond satisfactorily and with the necessary flexibility to the various market demands.
The object of this invention is to provide a scientific methodology with which to identify the performance characteristics of a tyre in relation to road handling, on the basis of previously defined design specifications.
The above object is achieved according to this invention by a method for determining the road handling of a tyre of a wheel for a vehicle, said tyre being made from selected mixes of rubber and reinforcing materials, said method comprising:
a) a first description of said tyre by means of a first, concentrated-parameter, physical model, said first physical model comprising a rigid ring which represents the tread band provided with inserts, a belting structure and corresponding carcass portion of said tyre, a disk which represents a hub of said wheel and beading of said tyre, principal springs and dampers connecting said rigid ring to said hub and representing sidewalls of said tyre and air under pressure inside said tyre, supplementary springs and dampers representing deformation phenomena of said belting structure through the effect of a specified vertical load, and a brush model simulating physical phenomena in an area of contact between said tyre and a road, said area of contact having a dynamic length 2a, 
b) a definition of selected degrees of freedom of said first physical model, and
c) an identification of equations of motion suitable for describing the motion of said first physical model under selected dynamic conditions, characterized in that it comprises
d) the definition of said concentrated parameters, said concentrated parameters consisting of the mass Mc and a diametral moment of inertia Jc of said rigid ring, the mass Mm and a diametral moment of inertia Jm of said disk, structural stiffnesses Kc and structural dampings Rc respectively of said principal springs and dampers, and residual stiffnesses Kr and residual dampings Rr respectively of said supplementary springs and dampers, wherein
said structural stiffnesses Kc consist of lateral stiffness Kcy between said hub and said belt, camber torsional stiffness Kcxcex8x between said hub and said belt and yawing torsional stiffness Kcxcex8z between said hub and said belt,
said structural dampings Rc consist of lateral damping Rcy between said hub and said belt, camber torsional damping Rcxcex8x between said hub and said belt and yawing torsional damping Rcxcex8z between said hub and said belt,
said residual stiffnesses Kr consist of residual lateral stiffness Kry, residual camber torsional stiffness Krxcex8x and residual yawing torsional stiffness Krxcex8z, and
said residual dampings Rr consist of residual lateral damping Rry, residual camber torsional damping Rrxcex8x and residual yawing torsional damping Rrxcex8z,
e) a description of said tyre by means of a second, finite-element model comprising first elements with a selected number of nodes, suitable for describing said mixes, and second elements suitable for describing said reinforcing materials, each first finite element being associated with a first stiffness matrix which is determined by means of a selected characterization of said mixes and each second element being associated with a second supplementary stiffness matrix which is determined by means of a selected characterization of said reinforcing materials,
f) a simulation on said second, finite-element model of a selected series of virtual dynamic tests for exciting said second model according to selected procedures and obtaining transfer functions and first frequency responses of selected quantities, measured at selected points of said second model,
g) a description of the behaviour of said first physical model by means of equations of motion suitable for representing the above dynamic tests for obtaining second frequency responses of said selected quantities, measured at selected points of said first physical model,
h) a comparison between said first and said second frequency responses of said selected quantities to determine errors that are a function of said concentrated parameters of said first physical model, and
i) the identification of values for said concentrated parameters that minimize said errors so that said concentrated parameters describe the dynamic behaviour of said tyre,
j) the determination of selected physical quantities suitable for indicating the drift behaviour of said tyre, and
k) the evaluation of the drift behaviour of said tyre by means of said physical quantities.
To advantage, said selected physical quantities are the total drift stiffness Kd of said tyre, in turn comprising the structural stiffness Kc and the tread stiffness Kb, and the total camber stiffness Kxcex3 of said tyre.
According to a preferred embodiment, said method also comprises
1) a definition of said brush model, said brush model having a stiffness per unit of length cpy and comprising at least one rigid plate, at least one deformable beam having a length equal to the length 2a of said area of contact and at least one microinsert associated with said beam, said microinsert consisting of at least one set of springs distributed over the entire length of said beam, said springs reproducing the uniformly distributed, lateral and torsional stiffness of said area of contact.
Preferably, said degrees of freedom referred to at previous point b) are composed of:
absolute lateral displacement ym of said hub, absolute yaw rotation "sgr"m of said hub and absolute rolling rotation xcfx81m of said hub,
relative lateral displacement yc of said belt with respect to said hub, relative yaw rotation "sgr"c of said belt with respect to said hub and relative rolling rotation xcfx81c of said belt with respect to said hub,
absolute lateral displacement yb of said plate, absolute yaw rotation "sgr"b of said plate and absolute rolling rotation xcfx81b of said plate, and
absolute lateral displacement ys of the bottom ends of said at least one microinsert.
According to another embodiment, said selected series of virtual dynamic tests referred to at previous point f) comprises a first and a second test with said tyre blown up and not pressed to the ground, said first test consisting in imposing a translation in the transverse direction y on the hub and in measuring the lateral displacement yc of at least one selected cardinal point of said belt and the force created between said hub and said belt in order to identify said mass Mc, said lateral stiffness Kcy, and said lateral damping Rcy, said second test consisting in imposing a camber rotation xcex8x on said hub and in measuring the lateral displacement of at least one selected cardinal point of said belt yc and the torque transmitted between said hub and said belt in order to identify said diametral moment of inertia Jc, said camber torsional stiffness Kcxcex8x, said camber torsional damping Rcxcex8x, said yawing torsional stiffness Kcxcex8z and said yawing torsional damping Rcxcex8z.
Preferably said selected series of virtual dynamic tests referred to at previous point f) also comprises a third and a fourth test with said tyre blown up, pressed to the ground and bereft of said tread at least in said area of contact, said third test consisting in applying to said hub a sideward force in the transverse direction Fy and in measuring the lateral displacement yc of said hub and of at least two selected cardinal points of said belt in order to identify said residual lateral stiffness Kry, said residual lateral damping Rry, said camber residual stiffness Krxcex8x, and said camber residual damping Rrxcex8x, said fourth test consisting in applying to said hub a yawing torque Cxcex8z and in measuring the yaw rotation of said hub "sgr"m and the lateral displacement yc of at least one selected cardinal point of said belt in order to identify said residual yawing stiffness Krxcex8z and said residual yawing damping Rrxcex8z.
According to another embodiment, said method also comprises
m) an application to said first physical model of a drift angle xcex1, starting from a condition in which said at least one beam is in a non-deformed configuration and said brush model has a null snaking "sgr"b,
n) the determination of the sideward force and the self-aligning torque that act on said hub through the effect of said drift xcex1 and which depend on the difference xcex1-"sgr"b and on the deformation of said at least one beam,
o) the determination of the deformation curve of said at least one beam,
p) an application of said sideward force and said self-aligning torque to said second, finite-element model in order to obtain a pressure distribution on said area of contact and
q) the determination of the sideward force and the self-aligning torque that act on said hub through the effect of said drift on said first physical model, that depend on the pressure distribution calculated in the previous step p),
r) a check, by means of said pressure distribution obtained in the previous step p), that said sideward force and said self-aligning torque are substantially similar to those calculated in previous step q),
s) a determination of the sideward force and of the self-aligning torque for said angle of drift, and
t) repetition of the procedure from step m) to step s) for different values of the drift angle xcex1 to obtain drift, force and self-alignment torque curves, suitable for indicating the drift behaviour under steady state conditions of said tyre, and
u) the evaluation of the steady state drift behaviour of said tyre.
According to another preferred embodiment, said method also comprises:
i) a simulation of the behaviour of said first physical model in the drift transient state by means of equations of motion reproducing selected experimental drift tests, and
ii) the determination, with a selected input of a steering angle imposed on said hub, of the pattern with time of the selected free degrees of freedom of said first physical model, of the sideward force and of the self-aligning torque in said area of contact in order to determine the length of relaxation of said tyre.
To advantage, said first elements of said second, finite-element model have linear form functions and their stiffness matrix is determined by means of selected static and dynamic tests conducted on specimens of said mixes, whereas the stiffness matrix of said second elements is determined by means of selected static tests on specimens of said reinforcing materials.
With the method according to this invention, three main results are obtained:
1. determination of the links between physical parameters of the tyre and its structural properties;
2. determination of the steady state drift behaviour of the tyre, without the need to build prototypes at this stage;
3. determination of the transient state behaviour of the tyre, when a generic law of motion is imposed on the hub, without the need to build prototypes at this stage.
These results have been achieved by the production of a very simple, first physical model, with only nine degrees of freedom, that manages to make allowance for the majority of the structural characteristics of the actual tyre.
The structural characteristics of the tyre are reproduced in the first physical model by means of an appropriate condensation of concentrated equivalent masses, stiffnesses and dampings.
In practice, the concentrated-parameter model is equivalent to a kind of dynamic concentration of the complex finite-element model, summarizing all its dynamic characteristics in a low number of mass, damping and stiffness parameters.
More specifically, it has been proven that this correspondence may be held valid in the range of frequencies between 0 and 80 Hz.
The method enables identification of the structural parameters needed for the complete description of the first physical model using simulated virtual numerical tests with a second, extremely detailed model built from finite element models (F.E.M.) reproducing the behaviour of the non-rolling tyre (not drifting).
One of the major advantages of the method according to the invention is that it partly dispenses with the need to construct physical prototypes and the resultant experimental tests in the iterative process of tyre determination, replacing this approach with virtual prototyping.
The tyre""s design parameters (characteristics of the mixes, inclination of the threads, shape of the sidewalls, width of the belt, etc.) are directly fed into the second, finite-element model which is extremely detailed.
The concentrated parameters of the first physical model are identified by minimizing the difference between the vibrational dynamic behaviour of the second, finite-element model of the non-rolling tyre and the corresponding response given by the first physical model.
The identification procedure defined comprises various operations that are executed in a precise, pre-established order. Starting from the transfer functions obtained by means of a series of virtual dynamic tests conducted on the non-rolling finite-element model, the masses, stiffnesses and dampings of the concentrated-parameter model are determined, providing a better description of the dynamic behaviour of the tyre.
Thus the identification procedure enables a link to be established between the design parameters (fed into the second finite-element model) and the condensed structural properties (contained in the first model with nine degrees of freedom), which is extremely useful in the construction of a tyre.
The method consists in linking the design parameters of the tyre, characteristics such as the mixture and the belt, to the structural parameters, for instance the structural stiffness and camber stiffness of the tyre, because the quantities appearing in the model used have a physical significance. This means that these quantities are directly linked to the design parameters, in other words the model used is a physical model. By so doing, any change to the design parameters of the tyre leads to a change of the parameters of the predictive physical model of the tyre and this change, in turn, produces a variation of the tyre""s structural parameters.
The model permits identification of the structural parameters starting from dynamic analysis made on the second, finite-element model of the non-rolling tyre. One requirement of the concentrated-parameter model is, in fact, that it be predictive of actual behaviour of the tyre.
One of the main advantages of the method according to the invention is that the concentrated parameters are not identified by means of experimental tests on prototypes, but by means of virtual dynamic tests on the finite-element model of the non-rolling tyre.
The method according to the invention uses a model of contact between tyre and road that enables forecasting of the drift curves at steady state. Also fed into the brush model, in addition to the longitudinal and transversal stiffness of the inserts of the tread, was their torsional stiffness, these stiffnesses being identified by means of numerical simulations on the second finite-element model, without any need for experimental tests.
The method according to the invention enables drift curves to be determined
by applying a drift angle xcex1 to the first physical model;
created in the area of contact on account of the drift are a sideward force and a self-aligning torque that act on the first physical model as forces acting on the hub and cause a lateral displacement and a snaking motion of the plate of the brush model;
because of the snaking motion "sgr"b and the lateral displacement of the plate, the forces set up in the contact area are modified; this results in a variation of the unconstrained degrees of freedom, among which those of the plate, and therefore of the forces acting of the first physical model.
With this procedure, after a certain number of iterations, a point is reached at which the degrees of freedom of the first physical model settle about a steady state value. In this situation, the sideward force and the self-aligning torque created in the area of contact and from which the drift curves may be obtained are determined.
The method according to the invention also enables transient state drift behaviour of the tyre to be evaluated, making allowance in the brush model for the dynamic deformations undergone by the inserts of the tread in this stage.
In this way, the length of relaxation of the tyre while drifting is determined upon variation of the running conditions (speed, vertical load, drift angle, etc.). This procedure is also implemented without any need for experimental testing.